Partial Actions and Partial Fixed Rings

Abstract

In this article, we consider a partial action α of a finite group G on a ring R which possesses an enveloping action. Properties of the fixed subring R ^α are studied. Among other results, under some assumptions, we describe the prime radical, the Jacobson radical, and the upper nil radical. We also study semisimplicity, von Newmann regularity, and Goldie conditions.

Key Words:

• Enveloping action
• Fixed subring
• Partial actions
• Prime and Jacobson radical
• Semisimplicity

2000 Mathematics Subject Classification:

• 16W22
• 16N99
• 17C20
• 16S35

ACKNOWLEDGMENTS

The authors were partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brazil). Some results of this article are contained in the Ph.D. thesis written by the third named author and presented to Universidade Federal do Rio Grande do Sul.

Notes

Communicated by S. Sehgal.